Riemannian Topology Meeting

Contribution List

10. A rigidity theorem for the action of the diffeomorphism group on spaces of psc metrics

Johannes Ebert

11/8/18, 9:20 AM

For a closed, simply connected $d$-dimensional manifold spin $M$, we study the action of the (spin) diffeomorphism group of $M$ on the space $\mathcal{R}^+ (M)$ of psc metrics on $M$. Our main result is that the homotopy class of the map $f^*: \mathcal{R}^+ (M) \to \mathcal{R}^+ (M)$ only depends on the cobordism class in $\Omega^{\mathrm{Spin}}_{d+1}$ of the mapping torus of $f$. When...

11. Spaces of riemannian metrics satisfying surgery stable curvature conditions

Jan-Bernhard Kordaß (Karlsruhe Institute of Technology (KIT))

11/8/18, 10:40 AM

We will introduce spaces of riemannian metrics on a smooth manifold satisfying a curvature condition given by a subset in the space of algebraic curvature operators. Provided this condition is surgery stable, which is a notion based on the work of S. Hoelzel guaranteeing the condition can be preserved under surgeries of a certain codimension, we can generalize several theorems from positive...

4. On the topology of the Teichmüller space of negatively curved Riemannian metrics

Gangotryi Sorcar (Einstein Institute of Mathematics, HUJI)

11/8/18, 11:35 AM

This talk is a survey on results concerning the space $T^{<0}(M)$, which we call the Teichmüller space of negatively curved Riemannian metrics on $M$. It is defined as the quotient space of the space of all negatively curved Riemannian metrics on $M$ modulo the space of all isotopies of $M$ that are homotopic to the identity. This space was shown to have highly non-trivial homotopy when $M$ is...

7. Extra twisted connected sums and their $\nu$-invariants

Sebastian Goette (University of Freiburg)

11/8/18, 2:10 PM

Joyce’s orbifold construction and the twisted connected sums by Kovalev and Corti-Haskins-Nordström-Pacini provide many examples of compact Riemannian 7-manifolds with holonomy $G_2$. We would like to use this wealth of examples to guess further properties of $G_2$-manifolds and to find obstructions against holonomy $G_2$, taking into account the underlying topological $G_2$-structures.

The...

3. Scalar curvature and the multiconformal class of a direct product Riemannian manifold

Saskia Roos (University of Potsdam)

11/8/18, 3:05 PM

For a closed, connected direct product Riemannian manifold $(M,g) = (M_1 \times \ldots \times M_l, g_1 + \ldots + g_l)$ we define its multiconformal class $[\![ g ]\!]$ as the totality $\lbrace f_1^2 g_1 + \ldots + f_l^2 g_l \rbrace$ of all Riemannian metrics obtained from multiplying the metric $g_i$ of each factor by a function $f_i^2:M \rightarrow \mathbb{R}_+$. In this talk we discuss how...

2. Orbifolds all of whose geodesics are closed

Christian Lange (University of Cologne)

11/8/18, 4:30 PM

Manifolds all of whose geodesics are closed have been studied a lot, but there are only few examples known. The situation is different if one allows in addition for orbifold singularities. In the talk we discuss such examples and their properties. In particular, we explain rigidity phenomena of the geodesic length spectrum and of metrics with all geodesics closed in dimension two.

9. Non-negative Ricci curvature and harmonic maps

David Wraith

11/9/18, 9:20 AM

Taking as our starting point the classic paper of Eells and
Sampson, we use harmonic maps as a tool to investigate spaces and moduli spaces of Ricci non-negative metrics, and also to study concordances between such metrics. In the first case, among other things, we recover some recent results of Tuschmann and Wiemeler. In the second case, we uncover an interrelationship between concordance,...

1. $\mathop{Spin}^c$ Dirac operators and the Kreck-Stolz s invariant.

Jackson Goodman (University of Pennsylvania)

11/9/18, 10:40 AM

We use the $\mathop{Spin}^c$ Dirac operator to generalize a formula of Kreck and Stolz for the s invariant of $S^1$ invariant metrics with positive scalar curvature. We then apply it to show that the moduli spaces of metrics with nonnegative sectional curvature on certain 7-manifolds have infinitely many path components. These include certain positively curved Eschenburg and Aloff-Wallach...

8. Moduli spaces of non-negatively curved metrics on homotopy $RP^5$s

David González Álvaro (University of Fribourg)

11/9/18, 11:40 AM

The goal of this talk is to discuss the following result: for a manifold homotopy equivalent to $RP^5$, the moduli space of metrics with non-negative sectional (resp. with positive Ricci) curvature has infinitely many path connected components. The proof involves various elements such as Brieskorn spheres, Grove-Ziller metrics, reduced eta-invariants and fixed point formulas. This is joint...

6. Positively curved manifolds with isometric torus actions

Michael Wiemeler (WWU Münster)

11/9/18, 2:30 PM

The classification of positively (sectional) curved manifolds is a long standing open problem in Riemannian geometry. So far it was a successful approach to consider the problem under the extra assumption of an isometric group action.

In this talk I will report on recent joint work with Lee Kennard and Burkhard Wilking in this direction. Among other things we show the following: Let $M$ be a...

5. Local flexibility of open partial differential relations

Bernhard Hanke (Augsburg University)

11/9/18, 3:30 PM

In his famous book on partial differential relations Gromov formulates an exercise concerning local deformations of solutions to open partial differential relations. We will explain the content of this fundamental assertion and sketch a proof.

We will illustrate this by various examples, including the construction of $C^{1,1}$-Riemannian metrics which are positively curved "almost everywhere"...